Shuji's fate in the anime is to walk an empty earth, with nothing at his side but an Ax-Crazyenergy being who "loves" him too much to end his suffering. It's strongly implied that said energy being gave him immortality, which makes the situation much worse.
Subverted in the manga. Shuji and Chise somehow leave the Earth in Chise, who has become some kind of spaceship....but Chise forgot humans need to eat.
Although, Food withstanding, Manga Shuji seems very acceptable to the idea of living/loving together in Spaceship Chise until the end. Wouldn't call it much of an And I Must Scream situation.
I wouldn't call it much of an And I Must Scream situation, considering Shuji seems to end the novel on a relatively positive note, "In the end the Earth made a noise that sounded like Chise's heartbeat. It was the last love song of this little planet...and us. It was our love song. We're going to fall in love. We're going to live."
Also considering from Wordof God at the end of the last novel: "In this story, Chise and Shuji are not happy, but they are not unhappy either...There is no hope, but there are memories and there may be a future." (although, if there may be a future, isn't there hope? Hm.)
In the manga version, there's a part where Shuji provides the narration box "This was the last time we were happy," after a date he had with Chise. He does this in the middle of the second volume. The series has seven volumes... and that claim isn't an exaggeration, as the rest of the second volume shows.